Question: Simplify the following expression: $ x = \dfrac{1}{p + 10} + \dfrac{-9}{10} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{1}{p + 10} \times \dfrac{10}{10} = \dfrac{10}{10p + 100} $ Multiply the second expression by $\dfrac{p + 10}{p + 10}$ $ \dfrac{-9}{10} \times \dfrac{p + 10}{p + 10} = \dfrac{-9p - 90}{10p + 100} $ Therefore $ x = \dfrac{10}{10p + 100} + \dfrac{-9p - 90}{10p + 100} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{10 - 9p - 90}{10p + 100} $ $x = \dfrac{-9p - 80}{10p + 100}$